Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

10th Edition

ISBN: 9780137538461

Author: Robert Hogg, Elliot Tanis

Publisher: PEARSON+

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Textbook Question

Chapter 5.4, Problem 4E

Generalize Exercise 5.4-3 by showing that the sum of ii independent Poisson random variables with respective means μ 1 , μ 2 , ... , μ n is Poisson with mean μ 1 + μ 2 + ... + μ n .

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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Chapter 5.4, Problem 3E

Chapter 5.4, Problem 5E

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Chapter 5 Solutions

Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)

Ch. 5.1 - Let X have a geometric distribution with parameter...Ch. 5.1 - Suppose that X is a continuous random variable...Ch. 5.1 - Prob. 3E Ch. 5.1 - Prob. 4E Ch. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 7E Ch. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...

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Generalize Exercise 5.4-3 by showing that the sum of ii independent Poisson random variables with respective means μ 1 , μ 2 , ... , μ n is Poisson with mean μ 1 + μ 2 + ... + μ n .

Solution Summary: The author explains that the moment generating function of X_i, is

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Chapter 5 Solutions